Assuming the function is
f(x) = x^4 + 3x^3-28x^2
Factorising, we get
f(x) = x^2(x+7)(x-4)
Therefore, there is a double root at x = 0 and singular roots at x = -7 and 4
double roots tend to bounce, kind of like the standard quadratic y = x^2
singular roots tend to cross, kind of like a straight line on a graph, y = mx + b
Therefore, it bounces at x = 0, and crosses at x = -7 and 4
In general, a root raised to an even power bounces, and a root raised to an odd power crosses.
